Math, asked by hemlalkumardas7665, 1 year ago

IN TRAINGLE ABC SEG BD BISECT ANGLE ABC IF AB =X BC=X+5 AD=X-2 DC=X+2 THEN FIND THE VALUE OF X

Answers

Answered by Robin09
10

Step-by-step explanation:

By angle bisector property

 \frac{ab}{bc}  =  \frac{ad}{dc}

 \frac{x}{x + 5}  =  \frac{x - 2}{x + 2}

x ( x + 2 ) = (x - 2)(x + 5)

 {x}^{2}  + 2x =  {x}^{2}  + 5x - 2x - 10

2x = 3x - 10

2x - 3x = -10

-x = -10

.°. x = 10

Answered by varadad25
9

Answer:

The value of x is 10 units.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

In △ABC,

Seg BD bisects ∠ABC,

AB = x

BC = x + 5

AD = x - 2

DC = x + 2

We have to find the value of x.

Seg BD bisects ∠ABC,

∴ By the property of angle bisector of triangle,

( AB / BC ) = ( AD / DC )

⇒ [ ( x ) / ( x + 5 ) ] = [ ( x - 2 ) / ( x + 2 ) ]

⇒ x ( x + 2 ) = ( x - 2 ) ( x + 5 )

⇒ x² + 2x = x ( x + 5 ) - 2 ( x + 5 )

⇒ x² + 2x = x² + 5x - 2x - 10

⇒ 2x = 3x - 10

⇒ 2x - 3x = - 10

⇒ - x = - 10

⇒ x = 10

The value of x is 10 units.

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Additional Information:

1. Angle bisector theorem:

When a ray bisects an angle, every point on the ray is equidistant from the both arms of the angle.

2. Angle bisector theorem of triangle:

When a ray bisects an angle of a triangle, the arms of the angle and the remaining two sides are in the proportion.

3. This theorem is based on Basic Proportionality Theorem ( BPT ).

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